Echoes, or distorted and delayed reflections of an incident signal, are produced wherever there are impedance mismatches in a transmission system. In the public switched telephone network (PSTN), impedance mismatches exist primarily at the 2-to-4 wire hybrid interfaces. In a typical end-to-end PSTN connection, echoes of the speech signal are returned to the talker via the transmission path on which the talker is listening (this is referred to as "talker" echo). Echoes can become annoying if they are loud; but more importantly, if they are sufficiently delayed and therefore distinguishable from sidetone (normal feedback of the talker's voice from the microphone to the speaker of a telephone handset), echoes can become intolerable.
In most landline PSTN connections, the delay is short and echoes do not impair the communication. In cellular mobile communications, however, both the speech coding process and radio transmission add significant delays to the signal path (a round trip delay of over 100 ms. is possible). This can result in a severe talker echo problem for the mobile terminal user. Note that the landline user is less prone to the problem of talker echo because there are practically no impedance mismatches at the mobile end to reflect the speech signal).
An echo canceller, in general, operates by modelling the impulse response of the echo path, and using this model to cancel out the echo component from the signal returning to the mobile (i.e. send-out signal). If the echo path is assumed to be linear, the common transversal tap FIR filter and LMS adaptation algorithm can be used. Normally, a large number of taps are required to cover the maximum circuit length of an echo path, determined by the last non-zero sample in its impulse response, which could reach 48 ms for some calls. However, the impulse response of a typical echo path, looking into the PSTN, contains only a few regions of non-zero sample magnitudes (hereby called active regions) which are related to the points of reflection in the transmission path caused by the 2-to-4 wire hybrid interfaces. With a non-sparse echo canceller, a large portion of the computation is spent on modelling the zero samples, or dormant regions, of the impulse response.